Problem: After an Indian attack on a wagon train in the mid-1800s, all that's left is a destroyed wagon with its wheel slowly rotating at constant speed. An ant happens to be on the periphery of the wheel. She also happens to be a very smart ant (truly a Newton of her kind). So she estimates the time it takes to rotate once (2.5 sec) and the diameter of the wheel (85 cm; a metric ant!) and does the math in her head (ants don't have calculators) to find the angular velocity and the distance turned through in 8 seconds. And wonder of wonders - she also computes the radial acceleration!

Solution (how the ant did it):

One rotation is two Pi radians, so...

It takes 2.5 sec to rotate once, so 8/2.5 = 3.2 revolutions.

The radial acceleration requires the tangential velocity:

Watch out! The ants may take over the world!